The cost of an audio system depreciates by rs.720 during the second year and by rs.648 during the third year.Calculate:
1) the rate of depreciation p.a.
2) the original cost of the audio system
3)the value of the audio system at the end of the third year .

Asked by rickykumar00001 | 1st Jan, 2016, 04:55: PM

Expert Answer:

1. L e t space apostrophe P apostrophe space b e space t h e space o r i g i n a l space cos t space o f space t h e space a u d i o space s y s t e m space a n d space apostrophe R apostrophe space b e space t h e space d e p r e c i a t i o n space r a t e. C o s t space o f space t h e space a u d i o space s y s t e m space a f t e r space o n e space y e a r equals R s.720 rightwards double arrow 720 equals P open parentheses 1 minus R over 100 close parentheses rightwards double arrow fraction numerator 720 over denominator open parentheses 1 minus R over 100 close parentheses end fraction equals P... left parenthesis 1 right parenthesis S i m i l a r l y comma space C o s t space o f space t h e space a u d i o space s y s t e m space a f t e r space s e c o n d space y e a r equals 648 equals P open parentheses 1 minus R over 100 close parentheses squared rightwards double arrow 648 over open parentheses 1 minus R over 100 close parentheses squared equals P... left parenthesis 2 right parenthesis C o m p a r i n g space e q u a t i o n s space left parenthesis 1 right parenthesis space a n d space left parenthesis 2 right parenthesis comma space w e space h a v e comma fraction numerator 720 over denominator open parentheses 1 minus R over 100 close parentheses end fraction equals 648 over open parentheses 1 minus R over 100 close parentheses squared rightwards double arrow 720 equals fraction numerator 648 over denominator open parentheses 1 minus R over 100 close parentheses end fraction rightwards double arrow open parentheses 1 minus R over 100 close parentheses equals 648 over 720 rightwards double arrow open parentheses 1 minus R over 100 close parentheses equals fraction numerator 720 minus 72 over denominator 720 end fraction rightwards double arrow open parentheses 1 minus R over 100 close parentheses equals 1 minus 72 over 720 rightwards double arrow 1 minus R over 100 equals 1 minus 1 over 10 rightwards double arrow R over 100 equals 1 over 10 rightwards double arrow R equals 10 percent sign  2. S u b s t i t u t i n g space t h e space v a l u e space R equals 10 percent sign space i n space e q u a t i o n space left parenthesis 1 right parenthesis comma space w e space h a v e comma fraction numerator 720 over denominator open parentheses 1 minus 10 over 100 close parentheses end fraction equals P rightwards double arrow fraction numerator 720 over denominator 9 over 10 end fraction equals P rightwards double arrow fraction numerator 720 cross times 10 over denominator 9 end fraction equals P rightwards double arrow P equals R s.800  3. V a l u e space o f space t h e space a u d i o space s y s t e m space a t space t h e space e n d space o f space t h e space t h i r d space y e a r equals P open parentheses 1 minus R over 100 close parentheses cubed equals 800 open parentheses 1 minus 1 over 10 close parentheses cubed equals 800 open parentheses 9 over 10 close parentheses cubed equals R s 583.20

Answered by Vimala Ramamurthy | 2nd Jan, 2016, 11:01: AM